If $\sqrt{\frac{2}{x} + 2} = \frac{3}{2}$, solve for $x$.
Answer: Squaring both sides of the equation yields $\frac 2x + 2 = \frac 94$. Subtracting $2$ from both sides gives $\frac 2x = \frac 14$, so $x = \boxed{8}$.